Optimal. Leaf size=18 \[ x-e^2 x \left (4+e^{7-x}+x\right ) \]
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Rubi [A] time = 0.06, antiderivative size = 34, normalized size of antiderivative = 1.89, number of steps used = 4, number of rules used = 3, integrand size = 29, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.103, Rules used = {6688, 2176, 2194} \begin {gather*} -e^2 (x+2)^2-e^{9-x}+e^{9-x} (1-x)+x \end {gather*}
Antiderivative was successfully verified.
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Rule 2176
Rule 2194
Rule 6688
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (1+e^{9-x} (-1+x)-2 e^2 (2+x)\right ) \, dx\\ &=x-e^2 (2+x)^2+\int e^{9-x} (-1+x) \, dx\\ &=e^{9-x} (1-x)+x-e^2 (2+x)^2+\int e^{9-x} \, dx\\ &=-e^{9-x}+e^{9-x} (1-x)+x-e^2 (2+x)^2\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.02, size = 26, normalized size = 1.44 \begin {gather*} x-4 e^2 x-e^{9-x} x-e^2 x^2 \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.54, size = 28, normalized size = 1.56 \begin {gather*} -{\left (x e^{9} + {\left ({\left (x^{2} + 4 \, x\right )} e^{2} - x\right )} e^{x}\right )} e^{\left (-x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.20, size = 22, normalized size = 1.22 \begin {gather*} -{\left (x^{2} + 4 \, x\right )} e^{2} - x e^{\left (-x + 9\right )} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 24, normalized size = 1.33
method | result | size |
risch | \(-x^{2} {\mathrm e}^{2}-4 \,{\mathrm e}^{2} x +x -x \,{\mathrm e}^{9-x}\) | \(24\) |
norman | \(\left (\left (-4 \,{\mathrm e}^{2}+1\right ) x \,{\mathrm e}^{x}-x^{2} {\mathrm e}^{2} {\mathrm e}^{x}-{\mathrm e} \left ({\mathrm e}^{4}\right )^{2} x \right ) {\mathrm e}^{-x}\) | \(37\) |
default | \(x +{\mathrm e} \left ({\mathrm e}^{4}\right )^{2} \left (-x \,{\mathrm e}^{-x}-{\mathrm e}^{-x}\right )-x^{2} {\mathrm e}^{2}+{\mathrm e}^{-x} {\mathrm e} \left ({\mathrm e}^{4}\right )^{2}-4 \,{\mathrm e}^{2} x\) | \(51\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.37, size = 33, normalized size = 1.83 \begin {gather*} -x^{2} e^{2} - 4 \, x e^{2} - {\left (x e^{9} + e^{9}\right )} e^{\left (-x\right )} + x + e^{\left (-x + 9\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.09, size = 19, normalized size = 1.06 \begin {gather*} -x\,\left (4\,{\mathrm {e}}^2+{\mathrm {e}}^{9-x}+x\,{\mathrm {e}}^2-1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.12, size = 22, normalized size = 1.22 \begin {gather*} - x^{2} e^{2} + x \left (1 - 4 e^{2}\right ) - x e^{9} e^{- x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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